Simplify the following expression: $\dfrac{144p}{72p^3}$ You can assume $p \neq 0$.
Explanation: $ \dfrac{144p}{72p^3} = \dfrac{144}{72} \cdot \dfrac{p}{p^3} $ To simplify $\frac{144}{72}$ , find the greatest common factor (GCD) of $144$ and $72$ $144 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $72 = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3$ $ \mbox{GCD}(144, 72) = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 = 72 $ $ \dfrac{144}{72} \cdot \dfrac{p}{p^3} = \dfrac{72 \cdot 2}{72 \cdot 1} \cdot \dfrac{p}{p^3} $ $\phantom{ \dfrac{144}{72} \cdot \dfrac{1}{3}} = 2 \cdot \dfrac{p}{p^3} $ $ \dfrac{p}{p^3} = \dfrac{p}{p \cdot p \cdot p} = \dfrac{1}{p^2} $ $ 2 \cdot \dfrac{1}{p^2} = \dfrac{2}{p^2} $